Here we provide the parts of the heat kernel expansion coefficients relevant to the high-temperature expansion of the one-loop free energy in a three dimensional space. It is these coefficients that determine the divergent and finite parts of the high-temperature expansion when \(\beta \rightarrow 0\) . We just employ the known expressions [1]}, [2]}, [3]}, [4]} for the heat kernel coefficients adapted to the operator \(H_G\)  (REF ). Notice that we did not check the general formulas for the coefficients \(a_k\)  presented in [1]}, [2]}, [3]}, [4]} save the terms at small \(k\) .
